Blood pressure (BP) is an important indicator of the state of cardiovascular health. BP estimation is an essential method to prevent the occurrence of hypertension. Currently, there is a strong focus on low power design for a wearable BP estimation device. This paper proposes a lightweight artificial neural network (ANN) for BP estimation and implements it on an ultra-low-power application-specific integrated circuit (ASIC). On the test set, the mean absolute error (MAE) and standard deviation (SD) of the estimated systolic BP and diastolic BP are 2.47 ± 3.48 mmHg and 1.45 ± 1.88 mmHg. Besides, in the case of 8-bit quantization, the MAE ± SD of the estimated systolic BP and diastolic BP are 12.41 ± 5.32 mmHg and 6.29 ± 3.03 mmHg respectively. The regression result R2 of overall SBP and DBP is 0.9702. This ASIC whose power is 19.72 µW is validated via the 0.18 µm CMOS process, occupying an area of 730 µmx 730 µm.